Control over spatial distributions and patterns of individual neurons and their neurites provides an essential tool for studying the meaning of neuronal network patterns. Moreover, the complete direction control of synaptic connections between cells in each neuronal network is also essential to investigate the detailed information on the relationship between the forward and feedback signaling among the cells. Here, we have developed a method for topographical control of the direction of synaptic connections within a living neuronal network using a new type of individual-cell-based on-chip cell-cultivation system with an agarose microfabrication technology. The advantages of this system include the ability to control positions and number of cultured cells as well as flexible control of the direction of elongation of axons and dendrites with stepwise melting of thin agarose layer coated on the cultivation chip with a focused infrared laser beam even during cultivation without any destructive damage on cells. Using this system, we succeeded in forming fully-direction controlled single-cell-based neuronal network from individual Rat hippocampal cells. In this meeting, we discuss the potential damage of heat to cells while stepwise melting of agarose and demonstrate the ability of our on-chip agarose microfabrication method for individual cell-based neural networks.